The 16 Nats Identity

π14 ≈ 2eπ
Coherence-Rupture-Regeneration Framework | Level-Dependent Ω (System 1 → System 2)
Cortical Hierarchy (Felleman & Van Essen)
System 1 (fast)   Transition   System 2 (slow)
Signal Propagation & Information Accumulation
Coherence
Rupture
Regeneration
1
Active Level
0.00
Information (nats)
0.10
Ω (current level)
1.00
exp(C/Ω) hier.
CRR Parameters
Level 1 Ω = 0.100
System 1 System 2
Global Ω Modifier 1.00×
← More S1 More S2 →
Signal Rate 1.0×
Noise Level 0.05
Cumulative Information 0.00 / 16.03 nats
eπ
Hierarchical Gain exp(C/Ω) 1.00 / 23.14
eπ
Level-Dependent Ω
Ω(n) = 0.1 × 1.132n
Rupture Condition
δ(now) when C ≥ Ω(n)
Critical Threshold
Icrit = 14·ln(π) ≈ 16 nats
Early levels (1-4): Low Ω, fast ruptures
Late levels (12-14): High Ω, slow integration